699 research outputs found
The apex of the family tree of protocols: Optimal rates and resource inequalities
We establish bounds on the maximum entanglement gain and minimum quantum
communication cost of the Fully Quantum Slepian-Wolf protocol in the one-shot
regime, which is considered to be at the apex of the existing family tree in
Quantum Information Theory. These quantities, which are expressed in terms of
smooth min- and max-entropies, reduce to the known rates of quantum
communication cost and entanglement gain in the asymptotic i.i.d. scenario. We
also provide an explicit proof of the optimality of these asymptotic rates. We
introduce a resource inequality for the one-shot FQSW protocol, which in
conjunction with our results, yields achievable one-shot rates of its children
protocols. In particular, it yields bounds on the one-shot quantum capacity of
a noisy channel in terms of a single entropic quantity, unlike previously
bounds. We also obtain an explicit expression for the achievable rate for
one-shot state redistribution.Comment: 31 pages, 2 figures. Published versio
Asymptotic State Discrimination and a Strict Hierarchy in Distinguishability Norms
In this paper, we consider the problem of discriminating quantum states by
local operations and classical communication (LOCC) when an arbitrarily small
amount of error is permitted. This paradigm is known as asymptotic state
discrimination, and we derive necessary conditions for when two multipartite
states of any size can be discriminated perfectly by asymptotic LOCC. We use
this new criterion to prove a gap in the LOCC and separable distinguishability
norms. We then turn to the operational advantage of using two-way classical
communication over one-way communication in LOCC processing. With a simple
two-qubit product state ensemble, we demonstrate a strict majorization of the
two-way LOCC norm over the one-way norm.Comment: Corrected errors from the previous draft. Close to publication for
One-shot entanglement-assisted quantum and classical communication
We study entanglement-assisted quantum and classical communication over a
single use of a quantum channel, which itself can correspond to a finite number
of uses of a channel with arbitrarily correlated noise. We obtain
characterizations of the corresponding one-shot capacities by establishing
upper and lower bounds on them in terms of the difference of two smoothed
entropic quantities. In the case of a memoryless channel, the upper and lower
bounds converge to the known single-letter formulas for the corresponding
capacities, in the limit of asymptotically many uses of it. Our results imply
that the difference of two smoothed entropic quantities characterizing the
one-shot entanglement-assisted capacities serves as a one-shot analogue of the
mutual information, since it reduces to the mutual information, between the
output of the channel and a system purifying its input, in the asymptotic,
memoryless scenario.Comment: 10 pages, 2 figures. Title changed due to new results on the one-shot
entanglement-assisted quantum communication. In addition, an error in the
previous version regarding the converse proof of the one-shot EAC capacity
has been correcte
Universal coding for transmission of private information
We consider the scenario in which Alice transmits private classical messages
to Bob via a classical-quantum channel, part of whose output is intercepted by
an eavesdropper, Eve. We prove the existence of a universal coding scheme under
which Alice's messages can be inferred correctly by Bob, and yet Eve learns
nothing about them. The code is universal in the sense that it does not depend
on specific knowledge of the channel. Prior knowledge of the probability
distribution on the input alphabet of the channel, and bounds on the
corresponding Holevo quantities of the output ensembles at Bob's and Eve's end
suffice.Comment: 31 pages, no figures. Published versio
Adaptively correcting quantum errors with entanglement
Contrary to the assumption that most quantum error-correcting codes (QECC)
make, it is expected that phase errors are much more likely than bit errors in
physical devices. By employing the entanglement-assisted stabilizer formalism,
we develop a new kind of error-correcting protocol which can flexibly trade
error correction abilities between the two types of errors, such that high
error correction performance is achieved both in symmetric and in asymmetric
situations. The characteristics of the QECCs can be optimized in an adaptive
manner during information transmission. The proposed entanglement-assisted
QECCs require only one ebit regardless of the degree of asymmetry at a given
moment and can be decoded in polynomial time.Comment: 5 pages, final submission to ISIT 2011, Saint-Petersburg, Russi
Round Complexity in the Local Transformations of Quantum and Classical States
A natural operational paradigm for distributed quantum and classical
information processing involves local operations coordinated by multiple rounds
of public communication. In this paper we consider the minimum number of
communication rounds needed to perform the locality-constrained task of
entanglement transformation and the analogous classical task of secrecy
manipulation. Specifically we address whether bipartite mixed entanglement can
always be converted into pure entanglement or whether unsecure classical
correlations can always be transformed into secret shared randomness using
local operations and a bounded number of communication exchanges. Our main
contribution in this paper is an explicit construction of quantum and classical
state transformations which, for any given , can be achieved using
rounds of classical communication exchanges but no fewer. Our results reveal
that highly complex communication protocols are indeed necessary to fully
harness the information-theoretic resources contained in general quantum and
classical states. The major technical contribution of this manuscript lies in
proving lower bounds for the required number of communication exchanges using
the notion of common information and various lemmas built upon it. We propose a
classical analog to the Schmidt rank of a bipartite quantum state which we call
the secrecy rank, and we show that it is a monotone under stochastic local
classical operations.Comment: Submitted to QIP 2017. Proof strategies have been streamlined and
differ from the submitted versio
Entanglement generation with a quantum channel and a shared state
We introduce a new protocol, the channel-state coding protocol, to quantum
Shannon theory. This protocol generates entanglement between a sender and
receiver by coding for a noisy quantum channel with the aid of a noisy shared
state. The mother and father protocols arise as special cases of the
channel-state coding protocol, where the channel is noiseless or the state is a
noiseless maximally entangled state, respectively. The channel-state coding
protocol paves the way for formulating entanglement-assisted quantum
error-correcting codes that are robust to noise in shared entanglement.
Finally, the channel-state coding protocol leads to a Smith-Yard
superactivation, where we can generate entanglement using a zero-capacity
erasure channel and a non-distillable bound entangled state.Comment: 5 pages, 3 figure
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